Perforation techniques are widely used in the oil and gas industry both for enhancing hydrocarbon production by minimizing sand production and for hydraulic fracture stimulation initiation. Citing a comprehensive review on the topic, “the process of optimizing stimulation treatments uses orientated perforations to increase the efficiency of pumping operations, reduce treatment failures and improve fracture effectiveness. Completion engineers develop oriented-perforating strategies that prevent sand production and enhance well productivity by perforating to intersect natural fractures or penetrate sectors of a borehole with minimal formation damage.” See Almaguer et al., “Orienting perforations in the right direction”, Oilfield Review, Volume 1, Issue 1, Mar. 1, 2002.
Hydraulic fractures initiate and propagate from positions around the circumference of the open borehole wall that offer the least resistance in terms of stress and rock strength conditions. If the formation material properties (e.g. elastic stiffness and strength) are isotropic and homogeneous and if the material is intact (free of natural fractures or flaws), it is generally accepted that the fracture initiation occurs at the locus around the borehole where the tensile stress is maximum. The stress conditions at the borehole wall in such formation depends on the local stress orientations and magnitudes (local principal stress tensor), the orientation of the borehole and a material property called Poisson's ratio (if the formation is assumed elastic).
One definition of an optimum perforation orientation is the orientation around the circumference of a subsurface borehole wall and the wellbore fluid initiation pressure that corresponds to the minimum principal stress at the borehole wall (rock mechanics convention is chosen here with positive compressive stress) reaching the tensile strength of the rock. Consequently, the optimum perforation orientation will ultimately lower the treatment pressure during hydraulic fracturing therefore lowering the energy requirement of a job. It will also result in a “smoother” fracture near the wellbore (i.e. less near wellbore tortuosity) in which proppant can be placed more effectively.
Perforation orientations may be designed with the following typical steps:    1. A rock property called Poisson's ratio v is estimated along the well most commonly using compressional Vp and shear Vs sonic log data from formula v=0.5(Vp2−2Vs2)/(Vp2−Vs2). Other methods may also be used as is known in the art.    2. The far-field stress field (or tensor), σ, and pore pressure, Pp, are characterized using direct or indirect stress measurements, leading to three principal stress directions and magnitudes (σ1>σ2>σ3) in the subsurface. When one principal stress is vertical and called σV, the following convention is used σH, and σh for, respectively, the maximum and minimum horizontal principal stresses. For a recent review of the existing methods, see Hudson, J. A., F. H. Cornet, R. Christiansson, “ISRM Suggested Methods for rock stress estimation Part 1: Strategy for rock stress estimation”, International Journal of Rock Mechanics & Mining Sciences 40 (2003) 991998; Sjoberg, J., R. Christiansson, J. A. Hudson, “ISRM Suggested Methods for rock stress estimation Part 2: Overcoring methods”, International Journal of Rock Mechanics & Mining Sciences 40 (2003) 9991010; Haimson, B. C., F. H. Cornet, “ISRM Suggested Methods for rock stress estimation Part 3: hydraulic fracturing (HF) and/or hydraulic testing of pre-existing fractures (HTPF)”, International Journal of Rock and U.S. Pat. No. 8,117,014 to Prioul et al., entitled “Methods to estimate subsurface deviatoric stress characteristics from borehole sonic log anisotropy directions and image log failure directions”.    3. Given known well orientation as a function of depth, defined by two angles (well azimuth and deviation), the principal stress tensor σ=[(σ1 0 0; 0 σ2 0; 0 0 σ3] can be transformed using tensor rotation into a wellbore frame for example using so-called TOH-frame stress tensor σTOH=[σxxTOH σxyTOHσxzTOH σxyTOH σyyTOH σyzTOH; σxzTOH σyzTOH σzzTOH]. The TOH (top of the hole) frame is a coordinate system tied to the tool/borehole. Hence, its x- and y-axes are contained in the plane perpendicular to the tool/borehole, and the z-axis is pointing along the borehole in the direction of increasing depth. The x-axis of the TOH frame is pointing to the top of the borehole, the y-axis is found by rotating the x-axis 90 degrees in the tool plane in a direction dictated by the right hand rule (thumb pointing in the positive z-direction). Given a known internal wellbore pressure, Pw, borehole stresses (or near-field) are then computed using well-known Kirsch analytical expressions, (See Ernst Gustav Kirsch. Die Theorie der Elastizitat and die Bedurfnisse der Festigkeitslehre. “Zeitschrift des Vereines Deutscher Ingenieure”, 42(29):797-807, 1898; Y. Hiramatsu and Y. Oka. “Stress around a shaft or level excavated in ground with a three-dimensional stress state”; Kyoto Teikoku Daigaku Koka Daigaku kiyo, page 56, 1962; Y. Hiramatsu and Y. Oka. “Determination of the stress in rock unaffected by boreholes or drifts, from measured strains or deformations”, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, volume 5, pages 337-353. Elsevier, 1968), for the total stresses at the borehole wall for an arbitrary orientation of the borehole relative to the far-field in-situ stress tensor, as follows in cylindrical coordinates:σrr=Pw,σθθ=σxxTOH+σyyTOH−2(σxxTOH−σyyTOH)cos 2θ−4σxyTOH sin 2θ−Pw,σzzTOH=σzzTOH−2v(σxxTOH−σyyTOH)cos 2θ−4vσxyTOH sin 2θ,σθz=2(σyzTOH cos θ−σxzTOH sin θ),σrθ=σrz=0,where v is the Poisson's ratio, θ is the azimuthal angle around the borehole circumference measured clockwise from a reference axis (e.g. TOH). Equations to compute borehole stresses away from the borehole wall at a desired radial position into the formation are also available.    4. Then, the ideal perforation orientation for tensile initiation is found for the azimuthal position θt and the wellbore fluid initiation pressure Pwinit where the minimum principal stress at the borehole wall is given by
            σ      t        =                                                      σ              zz                        +                          σ              θθ                                2                -                                                            (                                                                            σ                      zz                                        -                                          σ                      θθ                                                        2                                )                            2                        +                          σ                              θ                ⁢                                                                  ⁢                z                            2                                          =                        -          To                +        Pp              ,where To is the tensile strength of the rock and Pp is the pore pressure.    5. Once the optimum orientation is known a perforation tool is lowered in the well. The perforation tool perforates the well in an optimum orientation obtained from the previous step.
For a stress field with one principal stress that is vertical (σV), we consider the special cases of well orientations where the azimuthal position θt is always in a principal direction:    (a) For vertical wells, the azimuthal position θt is the minimum hoop stress (minimum of σθθ) which is always in the direction of the maximum horizontal principal stress, σH.    (b) For horizontal wells drilled in the direction of a principal stress direction (σH or σh), the azimuthal position θt is also the one given by the minimum hoop stress (minimum of σθθ), i.e. is pointing to the top of the hole if σV is greater than the horizontal stress orthogonal to the borehole, or to the side of the hole if σV is smaller than the horizontal stress orthogonal to the borehole.
If the well is deviated, in such a stress field the orientation is not aligned with a principal stress direction and there is no obvious solution for θt as it also depends on the wellbore fluid initiation pressure so the orientation is computed numerically. See Peska, P. & Zoback, M., Compressive and tensile failure of inclined well bores and determination of in situ stress and rock strength, Journal of Geophysical Research, 1995, 100, 12,791-12,811.
When the earth formation has material properties that are directions dependent, i.e. anisotropic, steps 1, 2 and 3 above are not valid anymore and depend on the anisotropy of the rock. Although some studies have been completed on the impact of the anisotropy on the borehole stress concentration (i.e. step 3), those studies have focused on the wellbore stability issues and mud weight requirements to prevent wellbore collapse (shear) and tensile fracturing (tensile), and not on a workflow to assess the best perforation orientation.